Parabolic Magnetoresistance from the Interaction Effect in a Two-Dimensional Electron Gas

A negative magnetoresistance proportional to $B^2$ is found in the two-dimensional electron gas of GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures. It is explained by the conductivity correction due to the electron interaction effect in disordered two-dimensional systems. The high-field electron lifetime, estimated both from the interaction effect and from the Shubnikov-de Haas oscillations, is much shorter than the zero-field lifetime, demonstrating the predominance of long-range potential fluctuations in high-mobility GaAs-${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ samples.